A charge is placed at the centre of the line joining two charges q and q. For the system of three charges to be in equilibrium, what should be the value of Q? 

Explanation

Here Q is in equilibrium as it is at the centre and net force on it is zero
For equilibrium of q, net force on it is zero
`1/(4 pi epsilon_0) (Qq)/((r//2)^2) + 1/(4 pi epsilon_0) (q^2)/(r^2) = 0`
where r is separation between q and q `implies Q = (-q)/(4)` .